{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "3688510d-476c-4ff6-9003-548b14b23dad",
   "metadata": {},
   "source": [
    "Chapter 09\n",
    "\n",
    "# 圆锥曲线的一般形式\n",
    "Book_3《数学要素》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08faf591-32df-45da-ad71-9f27fe35c410",
   "metadata": {},
   "source": [
    "这段代码的核心是利用数学上的圆锥曲线方程绘制不同类型的几何图形（如圆、椭圆、抛物线和双曲线），并在给定范围内以等高线的形式可视化这些图形。以下是详细的数学描述：\n",
    "\n",
    "---\n",
    "\n",
    "### 数学背景与公式\n",
    "\n",
    "圆锥曲线的通用方程为：\n",
    "$$\n",
    "Ax_1^2 + Bx_1x_2 + Cx_2^2 + Dx_1 + Ex_2 + F = 0\n",
    "$$\n",
    "其中：\n",
    "- $A$、$B$、$C$ 决定了曲线的类型，例如：\n",
    "  - 当 $B^2 - 4AC > 0$ 时，为双曲线；\n",
    "  - 当 $B^2 - 4AC = 0$ 时，为抛物线；\n",
    "  - 当 $B^2 - 4AC < 0$ 时，为椭圆或圆。\n",
    "- $D$、$E$ 决定曲线的位置和偏移；\n",
    "- $F$ 决定曲线的大小或开口宽度。\n",
    "\n",
    "---\n",
    "\n",
    "### 代码实现的功能\n",
    "\n",
    "1. **生成坐标网格**：\n",
    "   - 定义 $x_1$ 和 $x_2$ 的取值范围为 $[-5, 5]$，在这个范围内生成 500 个等间距点；\n",
    "   - 使用 `numpy.meshgrid` 创建二维网格，用于计算每个网格点上的方程值。\n",
    "\n",
    "2. **计算曲线值**：\n",
    "   - 对网格点 $(x_1, x_2)$ 代入圆锥曲线方程，计算 $z$ 值，即：\n",
    "     $$\n",
    "     z = A x_1^2 + B x_1 x_2 + C x_2^2 + D x_1 + E x_2 + F\n",
    "     $$\n",
    "\n",
    "3. **绘制等高线**：\n",
    "   - 通过 `matplotlib` 的 `contour` 函数绘制 $z = 0$ 的等高线，这条线表示方程的解。\n",
    "\n",
    "4. **设置图形属性**：\n",
    "   - 调整坐标轴比例、范围及刻度，添加辅助线（如 $x_1 = 0$ 和 $x_2 = 0$），增强可视化效果。\n",
    "\n",
    "5. **保存与显示**：\n",
    "   - 将绘制的图形保存为 `.svg` 格式文件，并在屏幕上显示。\n",
    "\n",
    "---\n",
    "\n",
    "### 不同类型曲线的实例\n",
    "\n",
    "- **圆**：\n",
    "  $$\n",
    "  x_1^2 + x_2^2 = 9 \\quad (A=1, B=0, C=1, D=0, E=0, F=-9)\n",
    "  $$\n",
    "\n",
    "- **椭圆**：\n",
    "  $$\n",
    "  \\frac{x_1^2}{4} + \\frac{x_2^2}{9} = 1 \\quad (A=4, B=0, C=9, D=0, E=0, F=-36)\n",
    "  $$\n",
    "\n",
    "- **旋转椭圆**：\n",
    "  $$\n",
    "  5x_1^2 + 4x_1x_2 + 5x_2^2 = 36 \\quad (A=5, B=4, C=5, D=0, E=0, F=-36)\n",
    "  $$\n",
    "\n",
    "- **抛物线**：\n",
    "  $$\n",
    "  x_2^2 - 4x_1 = 4 \\quad (A=0, B=0, C=1, D=-1, E=0, F=-4)\n",
    "  $$\n",
    "\n",
    "- **双曲线**：\n",
    "  $$\n",
    "  x_1^2 - x_2^2 = 2 \\quad (A=1, B=0, C=-1, D=0, E=0, F=-2)\n",
    "  $$\n",
    "\n",
    "- **特殊双曲线**（如 $x_1x_2 = 1$）：\n",
    "  $$\n",
    "  x_1x_2 = 1 \\quad (A=0, B=1, C=0, D=0, E=0, F=-1)\n",
    "  $$\n",
    "\n",
    "---\n",
    "\n",
    "### 输出结果\n",
    "\n",
    "每种类型的圆锥曲线均绘制在独立的图形中，展示了不同系数下的几何特性及其变化。这种实现方式便于观察和理解圆锥曲线在几何形态上的多样性和对称性。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c335b892-9b76-406f-83e0-3894ddf498cc",
   "metadata": {},
   "source": [
    "## 导入包"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6fd7ec34-baa3-4915-834b-5601328c3ab3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d4ce96f-4c69-43c9-b751-3482d0c5548c",
   "metadata": {},
   "source": [
    "## 可视化函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b06ae13c-b659-4658-ae77-c10952e16a1a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 圆锥曲线的一般形式\n",
    "# Ax1^2 + Bx1x2 + Cx2^2 + Dx1 + Ex2 + F = 0\n",
    "\n",
    "def conic_plot(A, B, C, D, E, F, title):  # 定义绘制圆锥曲线的函数，参数为方程系数和标题\n",
    "    x1 = np.linspace(-5, 5, 500)  # 生成 x1 的取值范围，从 -5 到 5，包含 500 个点\n",
    "    x2 = np.linspace(-5, 5, 500)  # 生成 x2 的取值范围，从 -5 到 5，包含 500 个点\n",
    "    x1, x2 = np.meshgrid(x1, x2)  # 生成网格点，用于绘制二维曲线\n",
    "\n",
    "    z = A * x1**2 + B * x1 * x2 + C * x2**2 + D * x1 + E * x2 + F  # 计算圆锥曲线的值\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=(6, 6))  # 创建绘图窗口，设置图形大小\n",
    "    ax.contour(x1, x2, z, levels=[0], colors='blue')  # 绘制等高线，曲线表示方程为 0 的解\n",
    "    plt.title(title)  # 设置图形标题\n",
    "    plt.xlabel('x1')  # 设置 x 轴标签\n",
    "    plt.ylabel('x2')  # 设置 y 轴标签\n",
    "    ax.set_aspect('equal', 'box')  # 设置坐标轴比例相同\n",
    "    ax.set_xlim(-5, 5)  # 设置 x 轴范围\n",
    "    ax.set_ylim(-5, 5)  # 设置 y 轴范围\n",
    "    ax.set_xticks(np.arange(-5, 6, 1))  # 设置 x 轴刻度\n",
    "    ax.set_yticks(np.arange(-5, 6, 1))  # 设置 y 轴刻度\n",
    "    plt.axhline(0, color='black', linewidth=0.5)  # 绘制 y=0 的辅助线\n",
    "    plt.axvline(0, color='black', linewidth=0.5)  # 绘制 x=0 的辅助线\n",
    "    plt.grid(True, linestyle='-', color='0.8', alpha=0.7)  # 添加网格线，设置样式和透明度\n",
    "    plt.savefig(title + '.svg')  # 保存图形为 SVG 格式文件\n",
    "    plt.show()  # 显示图形"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6a6bc475-939c-4bf2-aa12-3bf0a411039e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HOnXqYOXKlWjdurXsaEQu6coVYNkyYOlScWogLS3nY+7uQKNG4i/1Fi3E6QEZV2HI4ukpRmeiooABA8R9p06J0Zx164DffwdOnxbH338H/vtfcUqoUyegSxfxfCk0yk0khTIF46uvvpIdgcjlJScDixf7Yv16DWvXApmZOR+75x7xl3i7dsAjj4hJl5QjNBR4/nnxZhjAoUOimP32mygeR44A06eLt+BgoGtX4OmnxWRWIspNmYJBRHlLTxenPr75Bli+XIPVWj77Y7VrA088If7yvv9+DvHnl6YBNWqIt6FDxRUsq1aJ0aBly8TE0Y8/Bj7+2A0hIWHo2VPDCy+I0yhEJLBgECkqNhb46ivg22/FIleChipVrHj+eQ906+aGatVkJiw6SpcGnnpKvFmtYmLookXAzz8bOH3aA5MnA5MnizksL74oRjZ8fGSnJpKLBYNIIVYr8MMPwMyZwJYtOfdXqAD06AH06KHDx+cUIiMrc46Ag1gsQIcO4u3qVQNffnkeq1aVx+rVGrZsEd+XoUOB554D+vcXV98QFUd8CSJSQEICMG5czjyBLVvERM3OncWQ/alTYm5A3bo8DeJM3t7A449fxfLlBk6dAqZMAapUAVJTgRkzgDp1gGbNgJ9+EkuiExUnLBhELuzPP4EXXhALWU2eLFawDAkB3npLLCy1ZAnw+OOutzZFcRQcDIweDRw+LK486dpVlMBNm4AnnxTF46OPxH4sRMUBCwaRC9q0SVztUbeumGORmSkWfvrhB7FI1rhx4hcauR43N3H57w8/iJVFx44FAgLE7aFDgUqVgPHj/z1vhqhoYsEgchGGIVbXfPhhMay+cqX4ZdWtm1j86Y8/xF/FHK1QR0iIGHmKjxenTKpUEeuTvPkmEB4OjBol9lQhKopYMIhcwMaNoli0aiWKhKcn0K+fWHth4UKxyiapy9tbfD8PHRIjG/ffLzZxmzYNiIgQRePyZdkpiczFgkEk0Z49QNu2QPPmYrlqiwUYPFhs2DVjhtj7g4oOd3cxCrV7N/Drr0DDhmKF1WnTxPf6rbc4R4OKDhYMIglOnBCXlUZFiTUVPDzEktXHjomJgEVlHxDKm6aJVVV37AB++UVs0paSArzxhjiNMnv2zauwEqmIBYPIiVJTxaS/6tWBBQvEfT16iKHzzz5jsShuNE2sp7F7t/h5iIwEzp8HXn5ZlI41a2QnJCo4FgwiJzAM4LvvgGrVxFoJVqvYZGz3bnE/T4UUb25uwDPPAH//DXz4odh6PjYWaNNGrHUSFyc7IZH9WDCIHCw2VlwV8vzzwNmz4q/UpUvFFSP168tOR67E0xMYMkRM7h08WMzZ+PlnoGZNMT/DapWdkCj/WDCIHOT6dWDMGDHU/ccf4kqCyZNF4ejUiStu0u2VLSvm4vz5p9j59sYNMT+jTh2xsyuRClgwiBxgwwaxB8U774jJep07AwcPivkXFovsdKSKmjXFqqALFoj9Zv75R5xa69sXSEqSnY7ozlgwiEyUmio2uGrRQlwRcs894nTIkiViBUcie2mamJ9x6JBYSwMAvvwSqFULWL5cbjaiO2HBIDLJxo1iCHvmTPF+v35i0l6nTnJzUdHg5yfWRtm0CahaVWyA9/jjYnv4lBTZ6YhyY8EgKiSrFRg5UoxanDghNiZbu1b8MihdWnY6KmqaNgX27QOGDxejG3PmiD1rNm+WnYzoZiwYRIVw+DAQHQ28+664FLVPn5yJeUSOUrIk8N57YtQsIkIU22bNxERQLtBFroIFg6iA5s0TK3Hu3St2y1y6VJwb56gFOUvTpsD+/UDPnoCui0tZmzcXm6sRycaCQWSntDSgd2+gVy+xYdUjj4hRC861IBl8fYG5c4H/+z9RbrdsEZup/fab7GRU3LFgENnh6FGgcWPxgu7mJv5iXL0aCA6WnYyKu+7dxWhagwZAYqLY6+T11wGbTXYyKq5YMIjyafly8eJ94ABQvrxYn2DcOLHaIpErqFxZTPYcOFC8P2mSKBqJiXJzUfHEgkF0F4YBvP222JQqORl48EHxl2KLFrKTEeVmsQCffgrMny8mg65aBTzwgFhBlsiZWDCI7uD6dbHb6WuviaLRvz+wbh1QsaLsZER39uyzwLZtQHi4WPStcWMuzEXOxYJBdBvnz4tRiv/7P6BECWDWLODzz8WGVEQqqFsXiIkRV5ZcvQp07Cj2ODEM2cmoOGDBIMrDsWMeaNJEw44dQJkywJo1wH/+IzsVkf0CA8VpkpdeEpeyDh0KDBmicfInORwLBtEttmwBunULwYkTGqpUAbZvF38BEqnK0xOYPRuYNk28/9lnGl55pQKuX5ebi4o2Fgyif/nlF6BNGw3Jye5o3NjA1q1i3wci1Wka8OqrwPffA56eBtas8cGjj2rclZUchgWD6H/mzQOeeAK4cUPDI49cw5o1BsqVk52KyFxPPQWsXGnA19eGzZs1NGsGnDsnOxUVRSwYRAA++USszGmzAT17Gvjss7Pw9padisgxmjUDFiw4gwoVDPz5p1hy/ORJ2amoqGHBoGJv2jRg8GBxe9gw4MsvDZQoITcTkaNVr56OTZsMhIeLFWofflhczkpkFhYMKtYmTwZGjRK3X39d7FDpxv8rqJiIjAT++AOoVk1skNasGfDPP7JTUVHBl1IqtiZPFkt9Z91+800xEY6oOAkJATZsAGrVAs6cEWu/HD0qOxUVBSwYVCxNm5ZTLqZMAcaOlZuHSKYKFcQKtbVqAQkJomTExclORapTpmBMmTIFDRs2hK+vL4KCgtC5c2ccPnxYdixS0Kef5pwWmTQJGD1abh4iVxAUJEpGjRrA6dNAy5ZiRIOooJQpGBs3bsTAgQOxfft2rFmzBpmZmWjTpg2uXbsmOxop5JtvgFdeEbfHjRN7jBCREBQkdgmuUkWMYLRqBVy6JDsVqUqZufIrV6686f05c+YgKCgIu3fvxsMPPywpFalk2TLgxRfF7aFDxZwLIrpZcLAoGQ89BBw6BLRrJ0Y2fH1lJyPVKFMwbpWcnAwAKFu27G0/x2q1wmq1Zr+fkpICANB1HbquOzagiXRdh2EYSmUGXCv3li3A009rsNk0vPCCgXffNWAYeW/65Eq57aVq9qy8KuZW9fm+U+7QULF/SbNmGnbt0vDEEwaWLTOkb/Sn6vMNqJu9MHk1w1BvXz3DMNCpUydcuXIFf/zxx20/b8KECZg4cWKu+/fs2QNfheq4YRhIS0uDt7c3NIUuc3CV3MeOeaBbtxAkJ7ujefNrmDHj7B3XuXCV3AWhanbDMNC3b1988cUXyuVW9fnOT+79+y144YV7kJbmhs6dUzBt2gWpV1qp+nwD6mZPTU1F/fr1kZycjNKlS9v1WCULxsCBA7F8+XJs3rwZISEht/28vEYwQkNDcfnyZfj7+zshqTl0XUdcXBwiIiLgptAiDa6Q+8IFoEkTDXFxGh54wMDatcZdV+h0hdwFpWp2XdfRtm1brFq1Srncqj7f+c29YgXQqZMY/Xv9dQMTJsj7laHq8w2omz0pKQkBAQEFKhjKnSJ55ZVX8Msvv2DTpk13LBcAYLFYYLFYct3v5uam1DcYADRNY2473bgBdOkiJqtFRgK//qrBxyd/fzmo+nwDamdXMbeqz3d+cz/2GDBzJtC3L/DWWxruvVfD8887KWQeVH2+ATWzFyarMv9KwzAwaNAg/PTTT1i3bh0iIiJkRyIXZhjASy+Jrdb9/YHly8GNy4gK6KWXci7tfuklYOtWuXlIDcoUjIEDB+K7777DggUL4Ovri3PnzuHcuXO4fv267GjkgqZNA+bPB9zdgcWLxVLIRFRwb78tdhtOTxcjg6dOyU5Erk6ZgjFjxgwkJyejefPmqFixYvbbokWLZEcjF7NiBTBmjLj9ySfAI4/IzUNUFLi5iXVk6tYVc5u6dAH49x3diTJzMBSci0oSHDsGPPusOEXyn/8A/fvLTkRUdJQqBSxdCjRoAOzeDQwYAHz9NffwobwpM4JBdDfXrwNPPgkkJQGNGwMffyw7EVHREx4OLFokRjTmzgW++EJ2InJVLBhUZLzyCrB/v5jM+cMPQB4XEBGRCVq2FHMyAGDwYGDPHrl5yDWxYFCRMH8+8NVXYqh2wQKxBTUROc6rrwIdOgBWK/D008D/FkomysaCQco7cgTo10/cfuMNsUETETlW1imSSpXE3Kf+/fNeep+KLxYMUlp6upjUefUq0KwZ8PrrshMRFR9lywL/93/icvAFC4Bvv5WdiFwJCwYpbeJEYNcuoEwZ4LvvxAsdETlPkybAhAni9qBBYuVcIoAFgxS2ZQvwzjvi9uzZnHdBJMuYMUDTpkBqKvDCC4DNJjsRuQIWDFLStWtAz56ArosXtK5dZSciKr7c3YF58wAfH2DzZuCDD2QnIlfAgkFKGjNGTCwLCeF6F0SuICIip1iMGwccPCg3D8nHgkHK2bxZLAEOiEtT/fzk5iEioU8f4NFHxaWrffrwVElxx4JBSrlxQ+zmCAAvvgi0aSM3DxHl0DQxH8rXF9i2Dfj8c9mJSCYWDFLKlCnA4cNAhQrA9Omy0xDRrUJDgalTxe2xY7nranHGgkHKOHRIFAxAzLsoU0ZuHiLK28svAw8+KNanGTJEdhqShQWDlGAY4hr7jAygfXteNULkytzcgJkzxdUlS5YAy5fLTkQysGCQEn74AVi7FvDyEhM8uT00kWurXRsYNkzcHjxYzJ+i4oUFg1xeWhowYoS4PXo0ULmy3DxElD9vvAEEBwPHjwPvvSc7DTkbCwa5vGnTxESxsDBg5EjZaYgov3x9xf+/gJg/lZAgNw85FwsGubQzZ3JeoN59FyhZUm4eIrLPs88CjRuL1Xdfe012GnImFgxyaePGAdevixnpnNhJpB5Ny1nhc948YP9+uXnIeVgwyGUdOCBekABx/pYTO4nU1Lgx0K2buBps1CjZachZWDDIZb32mnhB6toVaNRIdhoiKozJk4ESJYBVq4D162WnIWdgwSCXtG0bsGyZuI5+0iTZaYiosCIjgf/8R9zO+uOBijYWDHJJr78ujj17AtWqyc1CROYYN05M1N62DVixQnYacjQWDHI5mzeLRbU8PHKKBhGpr2JFYMAAcXviRI5iFHUsGORyJk4Ux969gfBwqVGIyGQjRwLe3sDOnWI+BhVdLBjkUnbsAH7/XUwGGzNGdhoiMltQENCvn7jN+VVFGwsGuZSs3VJ79ODoBVFRNWIE4OkJbNkC/PGH7DTkKCwY5DIOHQJ+/lmsdzF6tOw0ROQoFSsCvXqJ21kr9VLRw4JBLuP998WxY0egenW5WYjIsUaMEH9M/Por8PffstOQI7BgkEu4eBH45htxO2vnVCIquu69F+jcWdz+8EOZSchRWDDIJcyaBVitQIMGYt8RIir6hg0Tx2+/BS5flpuFzMeCQdJlZAAzZ4rbQ4ZwzxGi4uKhh4D77wdu3AC++kp2GjIbCwZJ98svYlv2cuWAp56SnYaInEXTgFdeEbdnzABsNrl5yFwsGCRd1ujFSy8BFovcLETkXN27A2XKACdOAKtXy05DZmLBIKmOHRMLa2lazkZIRFR8lCwJvPCCuD17ttwsZC4WDJLq66/FsU0bLqxFVFz17SuOy5YB587JzULmUapgbNq0CR06dEBwcDA0TcPSpUtlR6JCsNmAefPE7T595GYhInlq1QIaNxavCd9+KzsNmUWpgnHt2jXUrVsXn376qewoZIK1a8XkzrJlxeJaRFR89e4tjvPmcZfVoqKE7AD2aNeuHdq1ayc7Bpkk6y+V7t05uZOouHv6aWDwYCA2Fti3T1y+SmpTqmDYy2q1wmq1Zr+fkpICANB1Hbquy4plN13XYRiGUpmBO+e+dg1YskQDoOHZZ3W40j9N1ecbUDd7Vl4Vc6v6fLta7tKlgQ4dNPz4o4bvvjNQt27uYQxXzJ1fqmYvTN4iXTCmTJmCiRMn5rr/5MmTSExMlJCoYAzDQFpaGuLi4qAptArVnXIvX+6Da9cqICQkA0FBJ3H8uKSQeVD1+QbUzW4YBmw2m5K5VX2+XTH3I4+Uwo8/VsT8+Ta8/PIJuN1yEt9Vc+eHqtlTU1ML/NgiXTDGjBmD4cOHZ7+fkpKC0NBQhIWFwd/fX14wO+m6jri4OERERMDt1v/jXNidcm/YIP4He+65EoiMrCwj3m2p+nwD6mbXdR3u7u5K5lb1+XbF3D17AqNHGzh/vgTOn6+ca9sAV82dH6pmT0pKKvBji3TBsFgssORxct/NzU2pbzAAaJpWZHJfvQqsXClud+umwc3N9dq8qs83oHZ2FXOr+ny7Ym5vbzHh+7vvgMWL3dC0ae7PccXc+aVi9sJkVedfSUXGypVi74HISKBuXdlpiMiVdO0qjkuW8GoS1Sk1gnH16lUcPXo0+/24uDjs27cPZcuWRaVKlSQmI3tkLV/SpQs3NiOim7VpI0Yy4uOBvXuB+vVlJ6KCUmoEY9euXbj//vtx//+uXxo+fDjuv/9+vPHGG5KTUX5lZgK//SZud+okNwsRuZ6SJYG2bcXtn3+Wm4UKR6mC0bx5cxiGkett7ty5sqNRPm3ZAly5AgQEANHRstMQkSvq0EEcly+Xm4MKR6mCQepbsUIcH30UcHeXm4WIXFP79uK4ezf3JlEZCwY5VdbVI1yQlYhup3z5nLkX3MJdXSwY5DTnzwP794vbbdrIzUJEri1rHgYLhrpYMMhp1q4Vx3r1gHLlpEYhIhfXurU4rl3Ly1VVxYJBTrN+vTi2bCk3BxG5vuhowMtLzME4dEh2GioIFgxymg0bxLFFC6kxiEgBXl5AkybidtZrB6mFBYOc4uxZ4OhRsbDWQw/JTkNEKnj4YXHctEluDioYFgxyii1bxLFOHcDPT24WIlJD1l4kmzfLzUEFw4JBTrF1qzjeujsiEdHtPPCAWC/n9GnxRmphwSCn2L5dHBs3lpuDiNTh4wPcd5+4nfUaQupgwSCHy8gQmxYBQKNGcrMQkVqyXjN27pSbg+zHgkEOFxsrtmf38wOqVJGdhohU0qCBOO7eLTcH2Y8Fgxxuzx5xrF8fcONPHBHZISpKHPfs4YJbquHLPTncn39qAMQKnkRE9qhVC/DwAJKSgPh42WnIHiwY5HAHDohj3bpycxCRejw9gRo1xO2svYxIDSwY5FCGkVMwsmaDExHZo3Ztcfz7b7k5yD4sGORQiYnuuHxZg6YB1avLTkNEKqpVSxxjYzW5QcguLBjkUMeOeQAAwsMBb2+5WYhITVmnSA4flpuD7MOCQQ514oQnAKBaNclBiEhZWaOf//zDK0lUwoJBDnXihBjBuPdeyUGISFmVK4uNElNTNVy+7C47DuUTCwY5VHy8KBiRkZKDEJGyLBYgJETcznpNIdfHgkEOdfp0CQBARITkIESktMqVxTHrNYVcHwsGOVRCgvhrIyxMchAiUlrWa0jWawq5PhYMcpjr14ErV8T50kqVJIchIqWFhorj2bMcwVAFCwY5zJkz4liypAF/f6lRiEhxWQXj/HlO8lQFCwY5zNmz4hgcLGaAExEVVMWK4njhAkcwVMGCQQ5z/rw4VqggNwcRqa98eXG8dIkjGKpgwSCHuXhRHMuVk5uDiNSXVTAuX3bnYluKYMEgh7l0SRwDA+XmICL1Zb2OpKe74do1uVkof1gwyGESE8XEi7JlJQchIuWVKgV4eIihiytXJIehfGHBIIdJThbHMmU4nklEhaNpyL4ajQVDDSwY5DApKeLo6ys3BxEVDX5+4pj12kKujQWDHCY1VRxZMIjIDD4+4nj1qtwclD8sGOQwaWni6O0tNwcRFQ1ZryVZry3k2uwqGPv378ekSZPw+eef41LWJQL/k5KSghdffNHUcKS2GzfEsWRJuTmIqGjIei25fl1uDsqffBeM1atX44EHHsDChQsxdepU1KhRA+vXr8/++PXr1zFv3jyHhPy3zz//HBEREfDy8kJUVBT++OMPh/83qWCsVnH09JSbg4iKhqzXkqzXFnJt+S4YEyZMwIgRI/DXX3/hxIkTGDlyJDp27IiVK1c6Mt9NFi1ahKFDh+K1117D3r170bRpU7Rr1w7x8fFOy0D5l5EhjiwYRGQGj/9tpJqZKTcH5U++C0ZsbGz2KRBN0/Dqq69i9uzZ6Nq1K5YtW+awgP/2/vvvo0+fPnjppZdQo0YNfPjhhwgNDcWMGTOc8t8n+9hs4ujOlX2JyARZryVZry3k2vK9a4zFYkFSUtJN9z3zzDNwc3ND9+7d8d5775md7Sbp6enYvXs3Ro8efdP9bdq0wdatW/N8jNVqhfVfY2kp/7u2Sdd16LruuLAm03UdhmEolRkADEP731GHStFVfb4BdbNn5VUxt6rPt4q53dwAQIPNpl52VZ/zwuTNd8GoV68e1q9fj6ioqJvu79atG3RdR8+ePQscIj8uXboEm82G8lkL0v9P+fLlce7cuTwfM2XKFEycODHX/V26dEGJEmrtyGez2eCu2FBAQkJJAG4YNuw6/PzU+p9Kxec7i6rZ9+/fj7Zt28qOYTdVn28Vcx84YAFQAp99ZsXPP6t3nkTF5zyzEOej8v1btn///ti0aVOeH3vmmWcAALNnzy5wkPzSbtn32zCMXPdlGTNmDIYPH579fkpKCkJDQ7FkyRL4Zy0JpwBd1xEXF4eIiAi4ualzZXG1ahqOHtXw3nuZaNpUndyqPt+Autl1XUfbtm2xatUq5XKr+nyrmPvJJ4GlS90weLAN/fvn/brvqlR9zpOSkhAQEFCgx+a7YHTp0gVdunTB77//jlatWuX6+DPPPJN9CsIRAgMD4e7unmu04sKFC7lGNbJYLBZYLJZc97u5uSn1DQZEsVItd9a+ATabWrkBNZ/vLCpnVzG3qs+3irkzM8VrSokSmlK5s6j4nBcmq92PfOyxx/Df//4X6enp2fddvHgRHTp0wJgxYwoc5G48PT0RFRWFNWvW3HT/mjVr0KRJE4f9d6ngsq4e+dePChFRgWVNqcvj70ZyQXYXjE2bNmHZsmVo2LAhYmNjsXz5ctSuXRtXr17F/v37HZEx2/Dhw/Hll1/i66+/xsGDBzFs2DDEx8ejX79+Dv3vUsFkvQhkLbhFRFQYWQXDy0tuDsofu2c6NmrUCHv37kW/fv0QFRUFXdcxadIkvPrqq7edC2GWbt264fLly3jzzTdx9uxZ1K5dG7/99hvCwsIc+t+lguGyvkRkpqwVPLk6sBoKdCnF4cOHERMTg5CQECQkJODQoUNIS0tDqVKlzM6Xy4ABAzBgwACH/3eo8LJ+HK5dk5uDiIqGrNeSrE3PyLXZfYrknXfeQXR0NFq3bo2//voLMTEx2Lt3L+rUqYNt27Y5IiMpKmsX1axdVYmICiM5WRy5Q7Ma7C4YH330EZYuXYpPPvkEXl5eqFWrFnbu3IknnngCzZs3d0BEUpWfnzgmJ6t1ORkRuaasgqHQKgPFmt2nSA4cOIDAwMCb7vPw8MC7776Lxx9/3LRgpL4yZcQxMVFuDiJSX0YGcPWq+GMl67WFXJvdIxi3lot/a9asWaHCUNESGCiuWb98WXIQIlJe1h8qmmZwBEMR6qz2QcrJWvzt4kW5OYhIfRcuiKO/v84NFBXBgkEOk7XAatYLAxFRQZ0/L45ly3IrVVWwYJDDVKggjmfPys1BROrL2iUiKEi9Tc6KKxYMcpjgYHG8eFHjcuFEVChnzohj+fIsGKpgwSCHCQwEPD3FNu1ZLw5ERAVx6pQ4VqjAgqEKFgxyGE0DgoPFi0F8vOQwRKS0rNeQihVZMFTBgkEOlVUw4uIkByEipZ04IY733MOCoQoWDHKo0NAMAMDx45KDEJGyDCPnNaRSpQy5YSjfWDDIocLCxIvB0aOSgxCRss6dExudubkZuOceFgxVsGCQQ4WHixeDw4clByEiZf3zjziGhwOenlKjkB1YMMihKlcW16cePgzouuQwRKSkgwfFsWpVuTnIPiwY5FCVKmXAw8PAtWs5l5kREdkjq2DUrCk3B9mHBYMcysMj56+Ov/6Sm4WI1JT12lGzpiE3CNmFBYMc7r77xPHPP+XmICL1GAZw4IC4nfVaQmpgwSCHq1tX/NWxb5/cHESknoQEsSOzuztQq5bsNGQPFgxyuHr1xHHvXqkxiEhBe/aIY/XqQMmScrOQfVgwyOHq1xfHI0eApCSpUYhIMbt2iWNUlNwcZD8WDHK4wEAgIkLcznqxICLKj5gYcWzYUG4Osh8LBjlFo0biuH273BxEpA7DAHbsELezXkNIHSwY5BTR0eK4bZvcHESkjsOHgcREwMsLqFtXdhqyFwsGOUWTJuK4dStX9CSi/Nm8WRwbNuQS4SpiwSCnqFcP8PERkzyzrmknIrqTP/4Qx6ZN5eaggmHBIKcoUQJ48EFxe8MGqVGISAGGkfNa0ayZ1ChUQCwY5DQtWojjunVycxCR6zt+HIiPF9sNZP1xQmphwSCneeQRcdywAcjMlBqFiFzc77+LY+PGQKlScrNQwbBgkNPUrw+ULQukpORcekZElJfVq8WxdWu5OajgWDDIadzdc14sVq6Um4WIXFdGRs4IRtu2crNQwbFgkFM9+qg4/vab3BxE5Lq2bhUjnYGBQIMGstNQQbFgkFO1bw9omtjAKCFBdhoickW//iqOjz4KuPG3lLL4rSOnCgrKWfJ32TK5WYjI9RgG8PPP4nbHjnKzUOGwYJDTdeokjkuWyM1BRK7n4EGx87KnZ84pVVKTMgVj8uTJaNKkCby9veHv7y87DhVCly7iuG4dcOWK3CxE5FoWLxbHVq0AX1+5WahwlCkY6enpeOqpp9C/f3/ZUaiQqlUDatUSM8WzhkKJiADghx/EsWtXuTmo8JQpGBMnTsSwYcNw3333yY5CJnj6aXFctEhuDiJyHQcPir2KPDxyTqWSukrIDuBIVqsVVqs1+/2UlBQAgK7r0BXa0lPXdRiGoVRm4M65n34aGD/eDWvWGDh/3kC5chIC3oaqzzegbvasvCrmVvX5dsXcCxZoADS0bm3A39/ItfOyq+bOD1WzFyZvkS4YU6ZMwcSJE3Pdf/LkSSQmJkpIVDCGYSAtLQ1xcXHQNE12nHy7U+4SJYDatUPw119e+PzzS3j++WRJKXNT9fkG1M1uGAZsNpuSuVV9vl0tt2EA8+aFAfBAy5bncfz41Tw+x/Vy55eq2VNTUwv8WKkFY8KECXkWgH+LiYlBgwKutDJmzBgMHz48+/2UlBSEhoYiLCxMqYmiuq4jLi4OERERcFPoovC75X7xRWD4cGDlykCMHx8gIWHeVH2+AXWz67oOd3d3JXOr+ny7Wu4tW4BTp9zg42PgP/8Jgrd3UK7PccXc+aVq9qSkpAI/VmrBGDRoELp3737HzwkPDy/w17dYLLBYLLnud3NzU+obDACaphW53D16ACNHAjt3ajh0SEPNmhIC3oaqzzegdnYVc6v6fLta7nnzxPHJJzX4+Nz+L3xXy20PFbMXJqvUghEYGIjAwECZEUiioCCxsucvvwBffw1Mny47ERHJcPVqzoTv3r3lZiHzKFOj4uPjsW/fPsTHx8Nms2Hfvn3Yt28frl7NfZ6O1PHii+L4zTdAerrcLEQkx6JFomRUqQI8/LDsNGQWZSZ5vvHGG5iXNYYG4P777wcArF+/Hs2bN5eUigrrsceA4GCxL8mSJUC3brITEZGzzZ4tji+9JPYqoqJBmRGMuXPnwjCMXG8sF2orUQLo00fcnjFDbhYicr49e4CdO8XaFzw9UrQoUzCo6PrPfwB3d2DjRuCvv2SnISJn+vRTcezaVczLoqKDBYOkCwkBOncWtz/5RGoUInKiixeBBQvE7UGD5GYh87FgkEsYPFgcv/0WuHRJbhYico5ZswCrFYiKAqKjZachs7FgkEto2hSoXx+4fh2YOVN2GiJytBs3ck6PDBvGyZ1FEQsGuQRNA/77X3H7k09E0SCiouu774Dz54HQ0JzND6loYcEgl/H000BYGHDhAjBnjuw0ROQoNhvw7rvi9tCh4goSKnpYMMhllCiRM4rx7rtARobcPETkGIsXA//8A5QpA/TtKzsNOQoLBrmUPn3EpWonToghVCIqWnQdmDxZ3B48GPD1lZuHHIcFg1yKtzfw6qvi9uTJQGam3DxEZK6lS4E//xTFYsgQ2WnIkVgwyOX07w+UKwccOyb2KCGiokHXgQkTxO0hQ8QpEiq6WDDI5ZQqBYwaJW6/+aa4Tp6I1LdoEXDgAODnBwwfLjsNORoLBrmkAQOAihWBkyfFYjxEpLaMDOD118XtESM4elEcsGCQSypZEhg/Xtx+6y0gJUVuHiIqnC++EKc9g4LEpalU9LFgkMt68UWgalWxdPjUqbLTEFFBpaTkzL144w3Ax0dqHHISFgxyWR4eOcXi/feB+Hi5eYioYKZMERubVa0qdk+m4oEFg1xap05As2Zi34KsiZ9EpI64OOCDD8TtadO4amdxwoJBLk3TxIuTpgELFwJ//CE7ERHZY/hwcSVYy5ZAx46y05AzsWCQy7v//pzlhAcN4uJbRKpYvVosrOXuDnz4IXdMLW5YMEgJkycDZcuKFQA/+0x2GiK6mxs3xB8EgDjWri03DzkfCwYpITBQTBQDgHHjgNOn5eYhojubOhU4ckSsZzNxouw0JAMLBinjpZeA6Gjg6lXglVdkpyGi2zl0CHj7bXH7ww/Fyp1U/LBgkDLc3MSqniVKiPO6ixfLTkREt9J1MWcqPR1o1w546inZiUgWFgxSyn335VyuOnAgcPmy3DxEdLPPPwc2bxZ7Cs2YwYmdxRkLBiln3DigRg3g/Hlu90zkSo4dy/kDYOpUICxMbh6SiwWDlOPlBcyZI06ZzJ/PUyVErsBmA3r1AtLSxOJ4/fvLTkSysWCQkho1yvlL6eWXgXPn5OYhKu7ef1+cGvHxyfkDgIo3/giQsiZMAOrVE/MwevcWk8uIyPn27gVee03c/vBDICJCahxyESwYpCxPT+C778Qpk5UrgY8/lp2IqPi5dg145hkgIwPo3FnsgkwEsGCQ4mrVAt57T9weNQrYvVtuHqLi5pVXgMOHgeBg4IsveNUI5WDBIOX17w906SKuu+/WDUhOlp2IqHj49tubJ1wHBspORK6EBYOUp2nAV1+JS+KOHRNDtIYhOxVR0RYbC/TrJ26/8QbQvLnUOOSCWDCoSChTBvj+e8DDA/jpp5zTJkRkvpQU4MknxSWprVuLtWmIbsWCQUXGAw+IGeyAmI+xbp3UOERFkq4DPXuKeRchIeLUiLu77FTkilgwqEjp3x944QXxIvj000BcnOxEREXLpEliLyBPT7HIXblyshORq2LBoCJF04CZM4EGDcT6GJ06AampslMRFQ0//QSMHy9uz5ghRg2JbkeJgnHixAn06dMHERERKFmyJCIjIzF+/Hikp6fLjkYuqGRJYMkSoEIF4MAB4NlnxTLGRFRwe/YAzz8vbg8ezPUu6O6UKBiHDh2CruuYNWsWYmNj8cEHH2DmzJkYO3as7GjkokJCxDCuxQL8+iswYoTsRETqOn0a6NBBTOps25aTqCl/SsgOkB+PPvooHn300ez3K1eujMOHD2PGjBmYPn26xGTkyho1AubNA7p3z1m+ePBg2amI1JKcDLRvDyQkiIXtFi0CSijxm4NkU/bHJDk5GWXLlr3j51itVlit1uz3U1JSAAC6rkNXaOMKXddhGIZSmQHXyP3UU8Dx48DYsW4YOtRAxYoGnnzyzo9xhdwFpWr2rLwq5lb1+c5PbqsVeOIJDQcOaKhQwcCyZQZ8feXt+6Pq8w2om70weZUsGMeOHcMnn3yC9+4yTjdlyhRMnDgx1/0nT55EYmKio+KZzjAMpKWlIS4uDppC6/C6Su6uXYG//iqHBQv80KMHYLUmoHHj67f9fFfJXRCqZjcMAzabTcncqj7fd8ttswHDh5fHunW+KFVKx8yZZ2CzWXH8uJPD/ouqzzegbvbUQsyS1wxD3pqHEyZMyLMA/FtMTAwaNGiQ/X5CQgKaNWuGZs2a4csvv7zjY/MawQgNDcXly5fh7+9fqOzOpOs64uLiEBERATeF9kB2pdw2G9Ctm4YlSzT4+hpYu9ZAVFTen+tKue2lanZd19G2bVusWrVKudyqPt93ym0YwMCBGmbN0uDhIUYuWreWEPQWqj7fgLrZk5KSEBAQgOTkZJQuXdqux0odwRg0aBC6d+9+x88JDw/Pvp2QkIAWLVogOjoas2fPvuvXt1gssFgsue53c3NT6hsMAJqmMXchuLkBCxYA7doBGzZoaNdOw6ZNQM2aeX++q+QuCJWzq5hb1ef7drkNAxg7Fpg1S1z2/e23Gtq2dZ2/uFV9vgE1sxcmq9SCERgYiMB87o5z5swZtGjRAlFRUZgzZ45S3yByDV5ewM8/A61aATExQMuWwKZNwL33yk5G5DreeguYOlXcnjlTbCBIVBBK/JZOSEhA8+bNERoaiunTp+PixYs4d+4czp07JzsaKaZ0aWDFCuC++4Bz54AWLcQGaUQEvPNOzkJa770H/Oc/cvOQ2pSY5Ll69WocPXoUR48eRUhIyE0fkziFhBQVEAD8/rsoF3//LXaBXL8eqFJFdjIieaZMEadGAODtt4Hhw+XmIfUpMYLRq1cvGIaR5xtRQQQFAWvXAjVqiEWEmjUTmzcRFTeGAbz5Zk65eOstYMwYuZmoaFCiYBA5QoUKYuSiVi2xiNDDDwN//ik7FZHzGIYoE1mnRd5+m1uvk3lYMKhYK18e2LABuP9+4MIFMZKxdavsVESOZ7OJS1GzJnS+/z5HLshcLBhU7AUGAuvWAU2aAElJQNu2GjZu9JYdi8hhrFZg2LDymDVLg6aJS1KHDZOdiooaFgwiAP7+wOrVwKOPAmlpGl5+uSLmzpWdish8SUnAY49pWLHCFx4eBhYu5NUi5BgsGET/U6oU8MsvQI8eBmw2DX36uOHNN8V5aqKiID4eaNoUWL9eQ6lSOpYvN/D007JTUVHFgkH0Lx4ewNy5Bl5++QoAMfmtVy8xpEyksl27gMaNgb/+AipUMDB//mm0bCk7FRVlLBhEt3BzA0aMuIzPP9fh7g58841Y/fPiRdnJiArmxx/FVVJnzwK1awPbthmoVStddiwq4lgwiG7j5ZeB334Tq39u3gw0bAjs2yc7FVH+6boYhXvqKeD6dTHHaMsWoFIl2cmoOGDBILqDNm2A7dvFKp8nT4orTf7v/2SnIrq75GSgc2exiBYgrhJZtkwUZiJnYMEguosaNYCdO4G2bcVfgc8+CwwZAqRzhJlc1IEDQIMGolBYLMDcuWKdixJKbA5BRQULBlE+lCkDLF+esxDRxx+LPUzi46XGIspl7lygUSPg6FFxKmTzZqBnT9mpqDhiwSDKJ3d3sZTyzz+LdTO2bQPq1ROXthLJlpoKvPAC0Lu3GGlr2xbYvVuMZBDJwIJBZKeOHcULd8OGwJUrQKdOwKBB4kWdSIZdu4CoKODbb8VVUG+9JSYoBwbKTkbFGQsGUQFUriyGnv/7X/H+Z5+JvxT37pWbi4qXzEwxqhYdDRw5AoSGir11xo0TRYNIJv4IEhWQpycwfTqwcqXYmfXvv8W578mTxQs/kSP9849Y2+K118TPW9eu4jLqpk1lJyMSWDCICqltW7HNe5cuQEaG+OsxOlrM5Ccym80GfPCBmP+zbZu47HTePOD774GyZWWnI8rBgkFkgnLlgMWLxaqf/v4558THj+cy42Sev/4CHnwQGD5czPlp1UoU2RdeADRNdjqim7FgEJlE04DnnwdiY8VE0IwMschRvXrAxo2y05HKrl8Xp0Luvx/YsQPw9RVbrK9ezVU5yXWxYBCZLDgYWLoUWLQIKF8eOHRIrJnxwgvA+fOy05Fqfv0VqFVLTObMzBRXLR08KLZY56gFuTIWDCIH0DTg6adFuejXT7z/7bdA1ari/DlXAaW7OXIEePxxoEMHIC4OCAkBfvpJlNd77pGdjujuWDCIHMjfH5gxQ+xn0qABkJIizp/fd5/4y9QwZCckV3Plirj8uVYtsXqshwcwcqQYtejSRXY6ovxjwSByggceEOfOv/wSCAoSlxh26AC0bCkmhBJZrWJ0q0oVsW9IRgbQrp2YxDl1KuDjIzshkX1YMIicxM0N6NNHDH2PGiU2oVq/XqwImnU6hYqfzEyxf0i1amJ0KzFRjF6sWCFW46xWTXZCooJhwSBystKlgXfeAQ4fzrm88IcfxC+Vnj3FJlVU9NlswP/9H1C7ttg/5ORJMUH4iy/EglmPPio7IVHhsGAQSRIWJhZI2r9fXNaq62IdjWrVRPE4eFB2QnKEjAwx4bdWLeDZZ0XRLFsWmDZNlMuXXuK26lQ0sGAQSXbffWKH1p07gfbtRdHI+gX05JNi7gapLy1N7FlTtaookIcPA2XKiI3J4uKAV18FSpaUnZLIPCwYRC6iYUNx1UBMjFjrwDDEZYmNG4v9JZYsEcPqpJaEBLF8fGio2HX3xAmx8uvbb4vb48aJ02ZERQ0LBpGLadBArHUQGwv06iUuU9y8GXjiCSAyUgylX7okOyXdiWEAW7aIUyBhYWIDvMREsQvvp5+KYjFmDIsFFW0sGEQuqmZNYM6cnF9GAQFiIuCoUWLRpeeeAzZt4loariQpSZwGqVsXeOghMYkzM1PsH/Ljj+Ly5IEDAW9v2UmJHI8Fg8jFBQeL4fRTp4CvvgLq1xdrJsyfDzRrJiaFTpkiPk7OZ7MBv/8uCl/FiuI0yIEDYj5F797A7t1iBOrJJwF3d9lpiZyHBYNIESVLAi++KBbm2rlTrKlRqpRYV2PsWDEU36qVhh9+8MWVK7LTFm2GAezZA7z6qoZmzcLRtq0b5s8HbtwQk3M/+gg4cwb4+mtRCImKI14MRaQYTRMTQhs2FCs//vijWKhp0yZg/XoN69eXx/jxBlq3Brp2FSuGBgbKTq0+wxCjEYsXi+dcrFeiASiBMmUMdO+uoVcv8X3hJmRELBhESvP1FcPwWQs1zZ+v45tvMnD4sAW//SZWgnRzE/MBOnYEHntMnFLhL8D8uX4d2LBB7Bvzyy/A6dM5HytZEmjf3kDLlufQq1d5lCzJJ5Xo31gwiIqIsDBg9Gjg6adPwWqtjJ9+csNPP4lVITdtEm8jRgDh4UDbtkDr1kCLFmKRJxJ0HfjrL2DtWmD1alEubtzI+XipUmJ/kCefFDudensbOH78GiwWaZGJXBYLBlERVKMG8Prr4u3ECWDZMvG2caN4f9Ys8aZp4oqHZs3EWhtNmoiJisVFZibw559iEuamTeL5ufUS4JAQMfKTtTmdl1fOx3TduXmJVKJMwejYsSP27duHCxcuoEyZMmjVqhWmTp2K4OBg2dGIXFp4OPDKK+Lt6lXxV/nq1eLKh4MHxQjHvn1iYiIgRkIaNRLrcURFAfXqFY1RDpsNOHZMTM7ctUssaLZrl1hh89+8vUXZat1ajPTUqsVTSkQFoUzBaNGiBcaOHYuKFSvizJkzGDFiBLp27YqtW7fKjkakDB8fMbT/+OPi/XPnxF/tmzaJhaEOHBBzOU6eBL7/PudxoaFiSfNatcToSPXqwL33irU5XO2Xb0aGGKX55x+xQ+3ff4vTHrGxwLVruT/f3z9ntdRmzcQkTU9PZ6cmKnqUKRjDhg3Lvh0WFobRo0ejc+fOyMjIgIeHh8RkROqqUAHo1k28AUBqqrgENuuv+z17xD4Zp06Jt99+u/nxpUsDERFi1KNSJeCee8S6HRUqAEFB4uqVgABz9tjQdSA5Gbh8Gbh4ETh/Hjh7VlwOevo0EB8vikV8/O2XVC9ZEqhTR4zMNGggRmqqVxcTYYnIXMoUjH9LTEzE/Pnz0aRJkzuWC6vVCqvVmv1+SkoKAEDXdegKnTzVdR2GYSiVGWBuGQqbvVQpMfGzRYuc+5KSxMjGX38BBw9qOHRIjA6cOqUhJUXsBrt//52/rqenAT8/cdWLt7f4RW+xiGXQ3dzEKMjevV5o3Rqw2Qykp4vJldevi9M6KSmi/BhG/oZLSpY0cO+9YmOxGjWAmjUN1KkjRl3yWuyqoN9qVX9WmNv5VM1emLyaYaiz0PCoUaPw6aefIi0tDY0bN8avv/6KgICA237+hAkTMHHixFz379mzB76+vo6MairDMJCWlgZvb29orjYefQfM7XzOzH7jhoZTp0rg9GkPJCSUwLlz4u3ChRK4fNkdly+7IynJHZmZ+c3REcAvd/2sUqV0lCljQ0CADeXKZSIoyIaKFTNRsWIGgoMzUalSBoKCbE45daPqzwpzO5+q2VNTU1G/fn0kJyejtJ2b50gtGLcrAP8WExODBg0aAAAuXbqExMREnDx5EhMnToSfnx9+/fXX236z8hrBCA0NxeXLl+Hv72/av8PRdF1HXFwcIiIi4KbQWC5zO5+rZTcMMfKQlJQzCnHtmhidsFrFfAmbTYxaTJvWHmPG/AYPDw0eHuJqDW9vMapSujTg5yfmS7jSJaGu9nznF3M7n6rZk5KSEBAQUKCCIfUUyaBBg9C9e/c7fk54eHj27cDAQAQGBqJq1aqoUaMGQkNDsX37dkRHR+f5WIvFAkser0Zubm5KfYMBQNM05nYiVXMDrpfd31+83Ymu6/j220z06KG5TO78crXnO7+Y2/lUzF6YrFILRlZhKIisgZd/j1AQERGRa1BikufOnTuxc+dOPPTQQyhTpgyOHz+ON954A5GRkbcdvSAiIiJ5lBinKVmyJH766Se0bNkS1apVw4svvojatWtj48aNeZ4CISIiIrmUGMG47777sG7dOtkxiIiIKJ+UGMEgIiIitbBgEBERkelYMIiIiMh0LBhERERkOhYMIiIiMh0LBhEREZmOBYOIiIhMx4JBREREpmPBICIiItOxYBAREZHpWDCIiIjIdCwYREREZDoWDCIiIjIdCwYRERGZjgWDiIiITMeCQURERKZjwSAiIiLTsWAQERGR6VgwiIiIyHQsGERERGQ6FgwiIiIyHQsGERERmY4Fg4iIiEzHgkFERESmY8EgIiIi07FgEBERkelYMIiIiMh0LBhERERkOhYMIiIiMh0LBhEREZmOBYOIiIhMx4JBREREpmPBICIiItOxYBAREZHpWDCIiIjIdCwYREREZDrlCobVakW9evWgaRr27dsnOw4RERHlQbmCMXLkSAQHB8uOQURERHegVMFYsWIFVq9ejenTp8uOQkRERHdQQnaA/Dp//jz69u2LpUuXwtvbO1+PsVqtsFqt2e+npKQAAHRdh67rDsnpCLquwzAMpTIDzC2Dqtmz8qqYW9Xnm7mdS9XshcmrRMEwDAO9evVCv3790KBBA5w4cSJfj5syZQomTpyY6/6TJ08iMTHR5JSOYxgG0tLSEBcXB03TZMfJN+Z2PlWzG4YBm82mZG5Vn2/mdi5Vs6emphb4sVILxoQJE/IsAP8WExODrVu3IiUlBWPGjLHr648ZMwbDhw/Pfj8lJQWhoaEICwuDv79/QSJLoes64uLiEBERATc3dc5qMbfzqZpd13W4u7srmVvV55u5nUvV7ElJSQV+rNSCMWjQIHTv3v2OnxMeHo5JkyZh+/btsFgsN32sQYMG6NGjB+bNm5fnYy0WS67HAICbm5tS32AA0DSNuZ1I1dyA2tlVzK3q883czqdi9sJklVowAgMDERgYeNfP+/jjjzFp0qTs9xMSEtC2bVssWrQIjRo1cmREIiIiKgAl5mBUqlTppvd9fHwAAJGRkQgJCZERiYiIiO5AnXEaIiIiUoYSIxi3Cg8Ph2EYsmMQERHRbXAEg4iIiEzHgkFERESmY8EgIiIi07FgEBERkelYMIiIiMh0LBhERERkOhYMIiIiMh0LBhEREZmOBYOIiIhMx4JBREREpmPBICIiItOxYBAREZHpWDCIiIjIdCwYREREZDoWDCIiIjIdCwYRERGZjgWDiIiITMeCQURERKZjwSAiIiLTsWAQERGR6VgwiIiIyHQsGERERGQ6FgwiIiIyHQsGERERmY4Fg4iIiEzHgkFERESmY8EgIiIi07FgEBERkelYMIiIiMh0LBhERERkOhYMIiIiMh0LBhEREZmOBYOIiIhMx4JBREREpmPBICIiItMpUzDCw8OhadpNb6NHj5Ydi4iIiPJQQnYAe7z55pvo27dv9vs+Pj4S0xAREdHtKFUwfH19UaFCBdkxiIiI6C6UKhhTp07FW2+9hdDQUDz11FN49dVX4enpedvPt1qtsFqt2e8nJycDAJKSkhwd1VS6riM1NRVJSUlwc1PmrBZzS6Bqdl3XkZmZqWRuVZ9v5nYuVbNn/b40DMPuxypTMIYMGYL69eujTJky2LlzJ8aMGYO4uDh8+eWXt33MlClTMHHixFz3R0REODIqERVQQECA7AhElIfLly/Dz8/PrsdoRkFqiUkmTJiQZwH4t5iYGDRo0CDX/YsXL0bXrl1x6dKl274o3TqCkZSUhLCwMMTHx9v9RMmUkpKC0NBQnDp1CqVLl5YdJ9+Y2/lUzc7czsXczqdq9uTkZFSqVAlXrlyBv7+/XY+VOoIxaNAgdO/e/Y6fEx4enuf9jRs3BgAcPXr0tgXDYrHAYrHkut/Pz0+pb3CW0qVLM7cTqZobUDc7czsXczufqtkLclpHasEIDAxEYGBggR67d+9eAEDFihXNjEREREQmUGIOxrZt27B9+3a0aNECfn5+iImJwbBhw9CxY0dUqlRJdjwiIiK6hRIFw2KxYNGiRZg4cSKsVivCwsLQt29fjBw50u6vM378+DxPm7gy5nYuVXMD6mZnbudibudTNXthckud5ElERERFkzoX4xIREZEyWDCIiIjIdCwYREREZDoWDCIiIjJdsS0Yqm//brVaUa9ePWiahn379smOc1dZlxR7eXmhYsWKeP7555GQkCA71l2dOHECffr0QUREBEqWLInIyEiMHz8e6enpsqPd1eTJk9GkSRN4e3vbvQKfM33++eeIiIiAl5cXoqKi8Mcff8iOdFebNm1Chw4dEBwcDE3TsHTpUtmR8mXKlClo2LAhfH19ERQUhM6dO+Pw4cOyY93VjBkzUKdOnexFqqKjo7FixQrZsew2ZcoUaJqGoUOHyo5yRxMmTMj1+7EgG40W24IBiO3fz549m/02btw42ZHybeTIkQgODpYdI99atGiB77//HocPH8bixYtx7NgxdO3aVXasuzp06BB0XcesWbMQGxuLDz74ADNnzsTYsWNlR7ur9PR0PPXUU+jfv7/sKLe1aNEiDB06FK+99hr27t2Lpk2bol27doiPj5cd7Y6uXbuGunXr4tNPP5UdxS4bN27EwIEDsX37dqxZswaZmZlo06YNrl27JjvaHYWEhOCdd97Brl27sGvXLjzyyCPo1KkTYmNjZUfLt5iYGMyePRt16tSRHSVfatWqddPvxwMHDtj/RYxiKiwszPjggw9kxyiQ3377zahevboRGxtrADD27t0rO5Ldfv75Z0PTNCM9PV12FLtNmzbNiIiIkB0j3+bMmWP4+fnJjpGnBx54wOjXr99N91WvXt0YPXq0pET2A2AsWbJEdowCuXDhggHA2Lhxo+woditTpozx5Zdfyo6RL6mpqca9995rrFmzxmjWrJkxZMgQ2ZHuaPz48UbdunUL/XWK9QjG1KlTERAQgHr16mHy5MlKDHufP38effv2xbfffgtvb2/ZcQokMTER8+fPR5MmTeDh4SE7jt2Sk5NRtmxZ2TGUl56ejt27d6NNmzY33d+mTRts3bpVUqriJTk5GQCU+nm22WxYuHAhrl27hujoaNlx8mXgwIF47LHH0KpVK9lR8u3IkSMIDg5GREQEunfvjuPHj9v9NZRYydMRCrL9u2yGYaBXr17o168fGjRogBMnTsiOZJdRo0bh008/RVpaGho3boxff/1VdiS7HTt2DJ988gnee+892VGUd+nSJdhsNpQvX/6m+8uXL49z585JSlV8GIaB4cOH46GHHkLt2rVlx7mrAwcOIDo6Gjdu3ICPjw+WLFmCmjVryo51VwsXLsSePXsQExMjO0q+NWrUCN988w2qVq2K8+fPY9KkSWjSpAliY2Nvu7longo9BuJCxo8fbwC441tMTEyej/3xxx8NAMalS5ecnDr/uT/66COjSZMmRmZmpmEYhhEXFyf1FIm9z/fFixeNw4cPG6tXrzYefPBBo3379oau60pkNwzDOHPmjFGlShWjT58+UjIbRsFyu+opkjNnzhgAjK1bt950/6RJk4xq1apJSmU/KHqKZMCAAUZYWJhx6tQp2VHyxWq1GkeOHDFiYmKM0aNHG4GBgUZsbKzsWHcUHx9vBAUFGfv27cu+T4VTJLe6evWqUb58eeO9996z63FFaqnwS5cu4dKlS3f8nPDwcHh5eeW6/8yZMwgJCcH27dvRqFEjR0XMU35zd+/eHcuWLYOmadn322w2uLu7o0ePHpg3b56jo96kMM/36dOnERoaiq1bt0oZ5rQ3e0JCAlq0aIFGjRph7ty5Bdq62AwFec7nzp2LoUOHIikpycHp7JOeng5vb2/88MMP6NKlS/b9Q4YMwb59+7Bx40aJ6fJP0zQsWbIEnTt3lh0l31555RUsXboUmzZtQkREhOw4BdKqVStERkZi1qxZsqPc1tKlS9GlSxe4u7tn32ez2aBpGtzc3GC1Wm/6mCtr3bo1qlSpghkzZuT7MUXqFImq27/nN/fHH3+MSZMmZb+fkJCAtm3bYtGiRU4vRUDhnu+sXmu1Ws2MlG/2ZD9z5gxatGiBqKgozJkzR1q5AAr3nLsaT09PREVFYc2aNTcVjDVr1qBTp04SkxVdhmHglVdewZIlS7BhwwZlywUg/i2yXj/yq2XLlrmuvujduzeqV6+OUaNGKVMurFYrDh48iKZNm9r1uCJVMPJL1e3fb83m4+MDAIiMjERISIiMSPmyc+dO7Ny5Ew899BDKlCmD48eP44033kBkZKTLT9JKSEhA8+bNUalSJUyfPh0XL17M/lhBrgt3pvj4eCQmJiI+Ph42my17vZQqVapk/+zINnz4cDz//PNo0KABoqOjMXv2bMTHx6Nfv36yo93R1atXcfTo0ez34+LisG/fPpQtW9alX0MGDhyIBQsW4Oeff4avr2/2XBc/Pz+ULFlScrrbGzt2LNq1a4fQ0FCkpqZi4cKF2LBhA1auXCk72h35+vrmmt9SqlQpBAQEuPS8lxEjRqBDhw6oVKkSLly4gEmTJiElJQU9e/a07wuZf7bG9e3evdto1KiR4efnZ3h5eRnVqlUzxo8fb1y7dk12NLvInoORX3/++afRokULo2zZsobFYjHCw8ONfv36GadPn5Yd7a7mzJlz27kOrq5nz5555l6/fr3saDf57LPPjLCwMMPT09OoX7++EpdMrl+/Ps/ntmfPnrKj3dHtfpbnzJkjO9odvfjii9k/I+XKlTNatmxprF69WnasAlFhDka3bt2MihUrGh4eHkZwcLDxxBNPFGi+S5Gag0FERESuoVivg0FERESOwYJBREREpmPBICIiItOxYBAREZHpWDCIiIjIdCwYREREZDoWDCIiIjIdCwYRERGZjgWDiIiITMeCQUQu4ezZs3j22WdRrVo1uLm5YejQobIjEVEhsGAQkUuwWq0oV64cXnvtNdStW1d2HCIqJBYMInKKixcvokKFCnj77bez79uxYwc8PT2xevVqhIeH46OPPsILL7wAPz8/iUmJyAzFcrt2InK+cuXK4euvv0bnzp3Rpk0bVK9eHc899xwGDBiANm3ayI5HRCZjwSAip2nfvj369u2LHj16oGHDhvDy8sI777wjOxYROQBPkRCRU02fPh2ZmZn4/vvvMX/+fHh5ecmOREQOwIJBRE51/PhxJCQkQNd1nDx5UnYcInIQniIhIqdJT09Hjx490K1bN1SvXh19+vTBgQMHUL58ednRiMhkLBhE5DSvvfYakpOT8fHHH8PHxwcrVqxAnz598OuvvwIA9u3bBwC4evUqLl68iH379sHT0xM1a9aUmJqICkIzDMOQHYKIir4NGzagdevWWL9+PR566CEAQHx8POrUqYMpU6agf//+0DQt1+PCwsJw4sQJJ6closJiwSAiIiLTcZInERERmY4Fg4iIiEzHgkFERESmY8EgIiIi07FgEBERkelYMIiIiMh0LBhERERkOhYMIiIiMh0LBhEREZmOBYOIiIhMx4JBREREpvt/R9IEG7f4cNAAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘制不同的圆锥曲线\n",
    "\n",
    "# 示例1: 正圆 A = 1, B = 0, C = 1, D = 0, E = 0, F = -9\n",
    "conic_plot(1, 0, 1, 0, 0, -9, \"Circle\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "42a1a0dc-8959-4991-ac68-9bb4c1e9019d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 示例2: 椭圆 A = 4, B = 0, C = 9, D = 0, E = 0, F = -36\n",
    "conic_plot(4, 0, 9, 0, 0, -36, \"Ellipse\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b796fb66-3325-4e9d-85a3-715866bdfb80",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 示例3: 旋转椭圆 A = 5, B = 4, C = 5, D = 0, E = 0, F = -50\n",
    "conic_plot(5, 4, 5, 0, 0, -36, \"Rotated Ellipse\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "57c79dbd-c0fc-4da4-942b-117675bc3bdd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 示例4: 抛物线 A = 0, B = 0, C = 1, D = -4, E = 0, F = 16\n",
    "conic_plot(0, 0, 1, -1, 0, -4, \"Parabola\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "304cd02a-a804-48a8-afd4-f8fac859ac34",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 示例5: A = 1, B = -2, C = 0, D = 0, E = 0, F = 0\n",
    "conic_plot(1, 0, 0, 0, 0, -4, \"Two parallel lines, vertical\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "49eff4d7-3b38-438a-819d-ea337cc34572",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 示例5: 旋转抛物线 A = 1, B = -2, C = 0, D = 0, E = 0, F = 0\n",
    "conic_plot(1, 2, 1, 0, 4, -8, \"Rotated Parabola\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "13dcf4d0-ce11-4b40-a334-bcf819b82bfc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 示例5: A = 1, B = -2, C = 0, D = 0, E = 0, F = 0\n",
    "conic_plot(1, 2, 1, 0, 0, -8, \"Two parallel lines, inclined\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "968791c9-35ea-4288-8d01-34b875f9df84",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 示例6: 双曲线 A = 1, B = 0, C = -1, D = 0, E = 0, F = -25\n",
    "conic_plot(1, 0, -1, 0, 0, -2, \"Hyperbola\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "dd468803-fa5a-4a40-9f4d-1173eb97f3fb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 示例10: 圆锥曲线 A = 0, B = 1, C = 0, D = 0, E = 0, F = -1\n",
    "conic_plot(0, 1, 0, 0, 0, -1, \"Hyperbola, x1x2 = 1\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "eb3e78de-46b7-45f0-b373-74abd379e57c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 示例7: 旋转双曲线 A = 1, B = 2, C = -1, D = 0, E = 0, F = -50\n",
    "conic_plot(1, 2, -1, 0, 0, -4, \"Rotated Hyperbola\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "83b2f944-1403-4d19-a281-11894d6edbc5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 示例8: 蜕化双曲线 A = 1, B = 0, C = -1, D = 0, E = 0, F = 0\n",
    "conic_plot(1, 0, -4, 0, 0, 0, \"Two intersecting lines\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "cb8516f3-38e4-4948-9348-167d88ad127e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 示例10: 圆锥曲线 A = 0, B = 1, C = 0, D = 0, E = 0, F = -1\n",
    "conic_plot(0, 1, 0, 0, 0, 0, \"Two intersecting lines, vertical and horizontal\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
